Objective Analysis of Sports

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RBI- has been a pretty important and valuable statistic…however recently the RBI has been becoming more and more discredited.

How We Know What Isn’t So
1. Misperception of Random Events
- Hot hand fallacy – Most statistical analysis shows that it’s not true. The evidence shows that the hot hand idea is false and that each shot is independent from the past shot. -Ex: Checked the statistics of the Philadelphia 76ers 1980 season and there was no correlation between making a shot after making the previous shot or missing a shot after missing the previous shot. There was no connection for each shot to the previous shot(s). - Severini Hot Hand Theory: The way most people use the hot hand theory is by comparing all the players on the floor together. Hot hand theory should be to give the ball to the player who has been most productive. Hot hand theory is “who is the best player THAT day”.

2. Missing Data (RBI?)
* Very hard to judge each coach and which coach is better than the other coach. Example- is Bill Belichick a better coach than Rex Ryan? You will never know because they never coached the same team and the same players, under the same circumstances. You cannot make conclusions without having the same circumstances and with this missing data.

3. Expectations
* How you view certain events is based on what you expect to occur before the event actually happens. * Example: Fielding in baseball.

4. Seeing what we want to see.
- You interpret things in a way that supports what you would like to be true. Can not rely on subjectivity.

5. Excessive impact of confirmatory information
- When you see something that supports a given point, it is more memorable and sticks in people’s minds more. -Ex. Roethlesberger holding the ball too long. He has been criticized for this and whenever he does, we quickly jump on that and criticize it. But when he makes a great play because he held the ball a little longer and a receiver broke open, we do not note the fact that this was because he held the ball a little longer.

- long run relative frequency
-ex. Probability Lebron James makes a free throw is .75 means that if he shoots a large number of free throws, he’ll make about 75% of them.

- Law of large numbers
- in large samples, “observed probabilities” will be close to the true probabilities.
- Law of Averages
- does not exist – more or less a myth. If a hitter is a good hitter, he will pick up the pace after a bad start but it has nothing to do with the previous results.

* .300 hitter

1. If two outcomes are mutually exclusive (they both can’t occur) than the probability that at least 1 occurs is the sum of the individual probabilities.
- prob of hit - .300
- prob of BB- .100
- prob of hit or walk = .300 + .100 = .400 (OBP)
2. The prob that two outcomes occur can never be greater than the prob that each occurs individually.

3. If two outcomes are independent (they don’t influence each other, nor are they influenced by common factors), than the probability that both occur is the product of the probabilities.
- prob that Bautista hits HR = .25
- prob that Fielder hits HR = .20
- prob that both hit HRs = (.20)(.25) = 0.05

Consider the coin flipping example:
1. total number of H
2. (max row) – (min row)
3. the largest streak (run( of either type
4. the number of runs
N “trials”
P probability of “success” on any trial

A typical longest streak of successes based on “complete randomness” is

- ln(n(1-p))
ln (p)

ex. Hitting streak
.300 hitter p=prob of at least 1 hit
4 AB in each game
prob. Of 0 hits = (.7) (.7) (.7) (.7) = 0.24
prob of at least 1...
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